Decide whether every of these statements is always, sometimes, or never true. ÂIf the is periodically true, draw and also describe a figure for i beg your pardon the explain is true and also another number for i m sorry the explain is not true.

You are watching: A rectangle is a square always sometimes never

A rhombus is a square A triangle is a parallelogram A square is a parallel AÂsquare is a rhombus A parallel is a rectangle A trapezoid is a quadrilateral

IM Commentary

The purpose of this job is to have students reason around different type of shapes based upon their specifying attributes and to recognize the relationship between different category of forms that re-superstructure some specifying attributes. In cases when the perform of defining features for the very first shape is a subset of the defining attributes of the 2nd shape, then the explanation will always be true.ÂIn instances when the list of defining qualities for the second shape is a subset of the defining attributes of the an initial shape, then the declaration will sometimes be true.

When this task is supplied in instruction, teachers should be prioritizing the standard for Mathematical exercise 6: resolve Precision. Students need to base their reasoning by introduce to next length, next relationships, and angle measures.


Solution

1. A rhombus is a square.

This is sometimes true. ÂIt is true when a rhombus has 4 best angles. ÂIt is not true when a rhombus does not have any kind of right angles.

Here is an example when a rhombus is a square:

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Here is an example when a rhombus is not a square:

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2. A triangle is a parallelogram.

This is never true. ÂA triangle is a three-sided figure. ÂA parallel is a four-sided number with two sets of parallel sides.

3. A square is a parallelogram.

This is always true. ÂSquares space quadrilaterals v 4 congruent sides and 4 appropriate angles, and also they also have two sets of parallel sides. Parallelograms space quadrilaterals v two sets of parallel sides. Because squares need to be quadrilaterals through two sets of parallel sides, then every squares are parallelograms.

4. AÂsquare is a rhombus

This is alwaysÂtrue. ÂSquares are quadrilaterals v 4 congruent sides. ÂSince rhombuses room quadrilaterals v 4 congruent sides, squares room by meaning also rhombuses. Â

5. A parallel is a rectangle.

This is sometimes true. ÂIt is true as soon as the parallelogram has actually 4 right angles. ÂIt is not true when a parallelogram has actually no best angles.

Here is an instance when a parallel is a rectangle:

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Here is an example when a parallelogram is not a rectangle:

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6. A trapezoid is a quadrilateral.

See more: 26 Mm Is How Many Inches - Convert 26 Millimeters To Inches

This is always true. ÂTrapezoids must have actually 4 sides, so they must always be quadrilaterals.